If God were the owner of the woods, you must start from the beginning when the main character wonders whose woods could they possibly be, and yet, he must stop to admire them because they are so lovely.

Under this point of view, the main character may be flirting with the possibility of exploring what "God" has in store for him. In fact, he may almost be convinced that something very good will come out of this exploration. Yet, he may also be questioning whether "God" would even know about this exploration; it is as if he wonders if he is even good enough to be noticed by God.

He will not see me stopping hereTo watch his woods fill up with snow

When the main character speaks of his horse wondering why, they are stopping by, it may very well be an allusion to his own heart/soul wondering why there is a need to find "God". The end of the poem is problematic to connect to God because the main character clearly moves away from it. In this case, we could either assume that the main character was too scared to try and ask God to consider him. Another explanation would be that the main character is hesitant to move on and prefers to stay and continue to admire the beauty of what may be in store for him.